Vector Control Algorithm for Efficient Fan-out RF Power Distribution

Managed by UT-Battellefor the Department of Energy

Vector Control Algorithm for Efficient Fan-out RF Power

Distribution

Yoon W. Kang

SNS/ORNL

Fifth CW and High Average Power RF Workshop

March 25-28, 2008

2 Managed by UT-Battellefor the Department of Energy Presentation_name

Motivation

Fan-out RF distribution with one higher power amplifier feeding multiple cavities may save construction/installation cost significantly especially in high power SRF linear accelerator projects

If a fixed power splitter is used with Vector Modulators in the fan-out system, power overhead is required for proper amplitude control

– Each cavity load needs one vector modulator that consists of two phase shifters and two hybrids

– The vector modulator dissipates the power difference between the input and the output

It is desirable to maximize the RF power to beam efficiency for further savings in operation

– Almost no power overhead is required - deliver only the beam power to the cavities with right RF voltages

An algorithm for fan-out RF distribution and control as a whole system is presented


Use of Vector Modulator

This gives the output amplitude and phase of the vector modulator in terms of the phase shift of each of the two phase shifters.

For a fixed input power, unused power PL is lost output

RF Control

Vector Modulator

input

2

2cos

21

21

out

in

out

A

A

P L


Comparison of RF Power Distribution Systems One klystron/one

cavity

Fan-out one klystron with Vector Modulators – power overhead requirement

Fan-out one klystron with no overhead power

PS

PS

Cavities

Amplifiers

RF Signals &Controls

VectorModulators+ Controls

Cavities

Amplifier

PS

RF Control

Cavities

Amplifier


Fan-out RF Distribution

1. Distributing RF power to N-loads through a transmission line network – a parallel connection

2. If the spacing Si = M(/2), Ls, Zs, and Bs can supply the specified voltages to the load – a series connection

3. A variation to the above case


Fan-out System Control using Transmission-line Sections and Reactive Loads

A set of specified voltages [Vi] can be supplied to the load cavities by adjusting the transmission-line impedances, lengths, and reactive loadings

This can be seen as a narrow-band multi-port impedance matching network

– Di = physical spacing between cavities

– di = length of transmission section between cavities

– Vi = voltage delivered to the cavity input

– Zi = transmission-line characteristic impedance

– Xi = reactive load


Network Parameters

A two-port network is used as a building block of a multi-port network synthesis

Various configurations are realizable: series fed, parallel fed, mixed, etc.– Network with parallel connections can be synthesized and analyzed by

using short-circuit admittance matrices [Z]– Network with series connections can be synthesized and analyzed by

using open-circuit impedance matrices [Y] Short-circuit admittance parameters [Y] are useful for network consists of

elements in parallel connections Using [Y], the voltages and currents of a two port network are related as

where

2

1

2

1

V

V

yy

yy

I

I

of

ri

)0(1

111

2

V

i V

Iyy

)0(2

112

1

V

r V

Iyy

)0(1

221

2

V

f V

Iyy

)0(2

222

1

V

o V

Iyy


System Equation (I)

PSS VYI

LTPS YYYY

PN

PPPtP VVVVV 1321

Consider an array of N-cavity loads connected to a transmission-line network. Let [VP] be the port voltage vector of a set of specific cavity excitations for an optimum operation.

where the short-circuit terminal admittance matrix of the whole system

[YP] = port admittance matrix for the cavities,

[YT] = short circuit admittance matrix of the transmission line network,

and [YL] = load admittance matrix.

The relation between the terminal currents [IS] and the terminal voltages [VP] is

[1]


System Equation (II)

Nin

in

in

in

p

Y

Y

Y

Y

Y

,

3,

2,

1,

000

000

000

000

The port admittance matrix only with the loads with no couplings between the cavities

If a cavity is mismatched, the port admittance matrix at the input of a cavity is found as:

cL

co

co

cL

oin djYdY

djYdYYY

sincos

sincos

)(1

)(1

z

zZZ oL

where Yo and dc are the characteristic impedance and the length of the transmission line connects the cavity to the network, respectively, YL is the cavity load impedance, and is the phase constant. The load is related to the reflection coefficient

11

332222

22221111

1111

cot000

0)cotcot(csc0

0csc)cotcot(csc

00csccot

NN

T

djY

dYdYjdjY

djYdYdYjdjY

djYdjY

Y

The transmission line admittance matrix


System Equation (III)The reactive load admittance matrix

N

L

jB

jB

jB

Y

00

00

00

2

1

1 SS YZ

The input impedance is found by selecting the element Zii in impedance matrix [Zs]

If the n-th terminal is used for feeding, only In =1 in the current matrix

01000 tSI

mTmm

Pm

Tmm

Pm

Tmm

Pm

Tmm

Pm

Tm

Pm

inmnm

S BjVdVYdVYdVYdVYjVyI )}csc()cot()cot()csc({ 111111

From the m-th element of the current vector is found as

(for m=1, 2, ..N) where n is the feed port index.

The above equations can be solved for a specified load voltages [VP] if any one out of the three parameters is given: transmission-line characteristic admittances, transmission-line lengths, and reactive loads. If a standard transmission line impedance YS is used, the lengths dm (dm-1), and reactive loads Bm can be found. YS

m-1 (YSm ) and, dm-1 (dm) are given so that the dm (dm-1), and reactive loads Bm are

found.

LTPS YYYY


Generalized RF Distribution

The lengths of the transmission line sections and the reactive loads are related to the phase shifts as

The transmission-line lengths and reactive loads can be realized by using high power phase shifters

nTn d )(cot 1

onLn YB

C1 C2 Ci-1

2

V1 V2 Vi-1 Vi

i-1

Z1 Z2 Zi-1 Zi

IS

Ci+1

Vi+1 Zi+1

CN-1 CN

VN-1 VNZN-1

-2i

r,1 r,2 r,i-1 r,N

r,i

r,i+1 r,N-1

z

m

m

o

o eV

V

ZzZ

ZzZz 2

)(

)()(

where voltage reflection coefficient (z)

If the loads are mismatched loads, the voltage standing wave in the transmission line section between the cavity and the input port is

)}(1{)()( zezVzV zjo

The voltage vector can be defined for no power (Vi = 0), forward power, or standing wave with the reflection coefficient (z)


Input Matching

The total power delivered to the loads is the sum of real power at the loads and must be identical to the output power of the klystron

C1 C2 C3

2

V1 V2 V3VN

i

Z1 Z2 Z3ZN

IS

CN-1

VN-1 ZN-1

-1

r,Nr,1 r,2 r,3 r,N-1

Pf

Pf

Pi

N

i

Pi

PPP YVYVVYVP2

1

2*

The feed terminal voltage is found from the above expression for a desired input impedance.

The voltage vectors are reconstructed to include the input that has an impedance specified. This constraints the input to be matched to the generator output

PNPf

PPPtP VVVVVV 321

C1 C2 C3

2

V1 V2 V3

i

Z1 Z2 Z3

IS

CN-1

VN-1 ZN-1

r,1 r,2 r,3 r,N-1

The voltage distribution is done, but the input of the network is not impedance matched to the source impedance

The input of the network can be impedance matched to a source with a specific source impedance by adding one more port


Simplified Fan-out System

PS

PhaseShifters

Cavities

KlystronRF Control

FP

DC

FP

DC

DC

Driverto PhaseShifters

Using proposed fan-out approach requires matching LLRF control system that must be developed


Procedure Summay and Consideration

Directional coupler at each cavity input measures cavity coupling (and load impedance)

A set of voltage vectors is defined for the required cavity RF voltages (amplitudes and phases)

The system equation is solved for the transmission line phase delays and the reactive loads at the ports

Phase shifters are tuned to the computed values The resultant voltages are read back and adjusted with FF and FB The above steps can be repeated

For a system with N- load cavities, followings are need to deliver the required voltages at the cavity coupler inputs with completely matched klystron amplifier output– N phase shifters between the terminals (transmission-line sections)– N+1 phase shifters at all terminals (reactive loads)

Fast high power phase shifters are needed Amplifier output control


Example12 cavities @ f = 805 MHz,cavities are critically coupled

Cavity Distance (m) Voltage (V) Zo () di (m) jBi ()

1 1.50 1.0000 0 50.0000 1.8742 - 0.0056i

2 1.50 1.0500 10 50.0000 1.8690 - 0.0026i

3 1.50 1.1000 20 50.0000 1.8673 + 0.0020i

4 1.50 1.1500 30 50.0000 1.8664 + 0.0056i

5 1.50 1.2000 40 50.0000 1.8659 + 0.0088i

6 1.50 1.2500 50 50.0000 1.8330 + 0.0715i

7 (3.9083 0 ) 50.0000 - 0.0544i

8 1.50 1.2500 50 50.0000 1.8330 + 0.0715i

9 1.50 1.2000 40 50.0000 1.8659 + 0.0088i

10 1.50 1.1500 30 50.0000 1.8664 + 0.0056i

11 1.50 1.1000 20 50.0000 1.8673 + 0.0020i

12 1.50 1.0500 10 50.0000 1.8690 - 0.0026i

13 1.50 1.0000 0 50.0000 1.8742 - 0.0056i

V1 V2

Vf

Vi

d1 d2

VN-1 VN

Zo

jB1 jB2 jBN+1

C1C1 CN

dN+1


Example - 4 Cavities

C2 C3 C4

VM1 VM2 VM3 VM4

1:1Splitter

2:1Splitter

2:1Splitter

C1

Amp

Using vector modulators

– Each VM employs two phase shifters and two hybrid power splitters

Using proposed fan-out approach

– Nine phase shifters are needed

– No circulator is needed

C1 C2 C3

d d2

jB1 jB2 jB3

V1 V2 V3 d

C4

jB4

V4 d

jBf

Zo AmpVf


Example – 4 Cavities4 cavities @ f = 402.5 MHz

cavities are critically coupled

Cavity Distance (m) Voltage (V) Zo () di (m) jBi ()

1 1.00 0.8000 0 50.00 1.5375 - 0.0070i

2 1.00 0.9000 20 50.00 1.5161 - 0.0017i

3 1.00 1.0000 40 50.00 1.5090 + 0.0065i

4 1.00 1.1000 60 50.00 1.4289 + 0.0175i

5 (50.00 input)

- 0.0233i

C1 C2 C3

d d2

jB1 jB2 jB3

V1 V2 V3 d

C4

jB4

V4 d

jBf

Zo AmpVf


Conclusion The proposed fan-out power distribution system can eliminate power

overhead to achieve efficient operation The fan-out system can be controlled as a whole to deliver the exactly

required amplitudes and phases of RF voltages at the cavities only with phase shifters

– Any cavities missing or need to be disabled in the system can be set to have 0 voltage vector

Phase delays and reactive loads at the cavity ports of the transmission line network are found by solving a network equation for a case using a standard transmission-line impedance

This system can also be seen as an adjustable narrow-band N-port power splitter or impedance matching network

The phase delays and reactive loadings can be realized by using high power fast phase shifters

– System bandwidth will still be dependent on the response of High power fast phase shifters are necessary

For practical waveguides, slight modification of the system admittance matrices will have to be made

Vector Control Algorithm for Efficient Fan-out RF Power Distribution

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